This is not true. What the author misses is that there are certain people who really aren't subject to the law of the land, and it's these people who the "subject to the jurisdiction" phrase is meant to address.
Those people are diplomats and occupying soldiers. Diplomats with immunity are not subject to US law, occupying soldiers operate under the laws of war and are not subject to civil laws. Use of the "subject to the jurisdiction" phrase is identifying these people, saying their children will not be citizens. There is no contradiction.
This construct was not new. At the time of adoption of the 14th this was the traditional way it worked. We inherited our rules from England, which operated the same way. The 14th only codified it in the Constitution to make it explicit with regard to ex-slaves. England did not change birthright citizenship until 1983.
We explicitly did NOT inherit our rules from England. We explicitly eschewed English Subject law in recognizing the condition of US Citizenship.
It's just that many Lawyers (such as William Rawle) Deliberately misled the public on this score in the early 19th century, and the consequences of their deliberately misleading the public have informed subsequent lawmakers in erroneous thinking.
The Claim that we followed English law was a tactic used by the early abolitionists to get slaves declared as citizens, and this is why they were deliberately misleading everyone regarding the condition of US Citizenship. (William Rawle was the President of the Pennsylvania Abolition society.)
This is why the Supreme Court said in Minor v Happersett that:
At common-law, with the nomenclature of which the framers of the Constitution were familiar, it was never doubted that all children born in a country of parents who were its citizens became themselves, upon their birth, citizens also. These were natives, or natural-born citizens, as distinguished from aliens or foreigners. Some authorities go further and include as citizens children born within the jurisdiction without reference to the citizenship of their parents. As to this class there have been doubts, but never as to the first.
These people pushing the English Law claims were those "Some authorities" which went "further". They were doing it in a good cause, but they were still lying about it, at least the original ones were.
“[S]ubject to the jurisdiction thereof” would not be necessary had the framers of the amendment intended to grant birthright citizenship. Had they intended that, they could simply have written that all persons born in the United States are citizens of the United States. That they did not tells us something.
The phrase “subject to the jurisdiction thereof” means “owing allegiance thereto” — which illegal aliens don’t. Their presence is by definition outside our laws and they still owe and retain allegiance to whatever rotten little satrapy they came from.
So of course they can be denied birthright citizenship without amending the Constitution. And they should be.